Christian Schilling

Pinning of Fermionic Occupation Numbers

The Pauli exclusion principle is a constraint on the natural occupation numbers of fermionic states. It has been suspected since at least the 1970s, and only proved very recently, that there is a multitude of further constraints on these numbers, generalizing the Pauli principle. Here, we provide the first analytic analysis of the physical relevance of these constraints. We compute the natural occupation numbers for the ground states of a family of interacting fermions in a harmonic potential. Intriguingly, we find that the occupation numbers are almost, but not exactly, pinned to the boundary of the allowed region (quasipinned). The result suggests that the physics behind the phenomenon is richer than previously appreciated. In particular, it shows that for some models, the generalized Pauli constraints play a role for the ground state, even though they do not limit the ground-state energy. Our findings suggest a generalization of the Hartree-Fock approximation.

Quasipinning and its relevance forN-fermion quantum states

Fermionic natural occupation numbers (NON) do not only obey Paulis famous exclusion principle, but are even further restricted to a polytope by the generalized Pauli constraints, conditions which follow from the fermionic exchange statistics. Whenever given NON are pinned to the polytopes boundary, the corresponding N-fermion quantum state |ΨN simplifies due to a selection rule. We show analytically and numerically for the most relevant cases that this rule is stable for NON close to the boundary, if the NON are nondegenerate. In case of degeneracy, a modified selection rule is conjectured and its validity is supported. As a consequence, the recently found effect of quasipinning is physically relevant in the sense that its occurrence allows to approximately reconstruct |ΨN, its entanglement properties, and correlations from one-particle information. Our finding also provides the basis for a generalized Hartree-Fock method by a variational ansatz determined by the selection rule.

Hubbard model: Pinning of occupation numbers and role of symmetries

Fermionic natural occupation numbers do not only obey Paulis exclusion principle, but are even further restricted by so-called generalized Pauli constraints. Such restrictions are particularly relevant whenever they are saturated by given natural occupation numbers

Pinning of fermionic occupation numbers: General concepts and one spatial dimension

\vec{\lambda}=(\lambda_i)

Natural Extension of Hartree–Fock Through Extremal 1-Fermion Information: Overview and Application to the Lithium Atom

. For few-site Hubbard models we explore the occurrence of this pinning effect. By varying the on-site interaction

Natural orbitals and occupation numbers for harmonium: Fermions versus bosons

U

Pinning of fermionic occupation numbers: Higher spatial dimensions and spin

for the fermions we find sharp transitions from pinning of

Quantum marginal problem and its physical relevance

\vec{\lambda}

Influence of the fermionic exchange symmetry beyond Pauli's exclusion principle

to the boundary of the allowed region to nonpinning. We analyze the origin of this phenomenon which turns out be either a crossing of natural occupation numbers

The quantum marginal problem

\lambda_{i}(U), \lambda_{i+1}(U)